Related papers: Localized patterns and hole solutions in one-dimen…
The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a…
In this paper, we present a general methodology for investigating the linear stability of localized solutions in PDEs and nonlocal equations on $\mathbb{R}^m$. More specifically, we control the spectrum of the Jacobian…
We propose an Ensemble of Robust Constrained Local Models for alignment of faces in the presence of significant occlusions and of any unknown pose and expression. To account for partial occlusions we introduce, Robust Constrained Local…
This work deals with two real scalar fields in two-dimensional spacetime, with the fields coupled to allow the study of localized configurations. We consider models constructed to engender geometric constrictions, and use them to…
An elastic sheet lying on the surface of a liquid, if axially compressed, shows a transition from a smooth sinusoidal pattern to a well localized fold. This wrinkle-to-fold transition is a manifestation of a localized buckling. The…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
Simple models for unitary black hole evolution are given in an effective Hilbert-space description, parameterizing a possible minimal relaxation of locality, with respect to semiclassical black hole geometry.
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…
A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback…
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
This book chapter gives an introductory review of a numerical framework for finding static and stationary vacuum black hole solutions. Such methods may be applied to explore the exotic space of higher dimensional black holes that are…
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…
We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long range interaction represented by a `soft' Coulomb…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case has been treated comprehensively by Amari 30 years ago, two-dimensional neural…
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…